A central Florida police chief who was criticized for his agency's initial investigation of Trayvon Martin's shooting death has been fired by a city manager, who said the chief had lost the trust of officials.

Sanford City Manager Norton Bonaparte said in a statement that he relieved Chief Bill Lee of duty because the manager said he "determined the police chief needs to have the trust and respect of the elected officials and the confidence of the entire community."

"We need to move forward with a police chief that all the citizens of Sanford can support. I have come to this decision in light of the escalating divisiveness that has taken hold of the city," Bonaparte said.

Sara Brady, a spokeswoman for the former chief, said Lee and Bonaparte met Wednesday morning to discuss his termination.

"They had a discussion this morning, but the details were not worked out, and that is how it was left," Brady said.

The initial lack of an arrest following the fatal shooting of Martin, an unarmed black teenager, by neighbourhood watch volunteer George Zimmerman in February led to protests across the nation and spurred a debate about race and the laws of self-defence. Zimmerman's father is white and his mother is from Peru.

Trayvon Martin, 17, was walking home from the convenience store when he was fatally shot. (Reuters)

The local prosecutor recused himself from the case, prompting Gov. Rick Scott to appoint special prosecutor Angela Corey, who charged Zimmerman in April with second-degree murder. The 17-year-old Martin was fatally shot following a Feb. 26 altercation with Zimmerman, who claims self-defence and has pleaded not guilty.

City previously rejected resignation

Lee took a leave of absence in March and offered his resignation in April. The city council rejected Lee's resignation by a 3-2 vote. Several council members indicated they wanted to let a Department of Justice review of the police investigation play out before making a final decision.

Martin's family and legal team addressed Lee's firing during a news conference at the National Association of Black Journalists' annual convention in New Orleans.

"The family's response and statement is that the city manager of Sanford had an internal investigation into the matter concerning Bill Lee," attorney Benjamin Crump said. "He concluded that investigation and made his decision. The parents of Trayvon Martin respect the decision of the city manager. They remain vigilant in getting justice for their son and the tragedy that claimed his life."

In May, Rick Myers took over as Sanford's interim police chief, saying he wanted to heal the emotional wounds caused by Martin's death. He has said he would reach out to people in Sanford who feel they've been ignored by the police.

Bonaparte said in a statement that he had been in contact with the Police Executive Research Forum about the search for a successor to Lee.

Lee will receive three months of severance and one week's salary, in addition to any earned time off, under his contract.

"I wish Chief Lee all the best in his future endeavors," Bonaparte said.